Reports found results of the SLT trials were erratic, with 10-year-olds consistently outperforming 14-year-olds in some tests. Photograph: Alamy

A new testing system to replace Sats in state schools has been hit by "substantial and fundamental" problems, according to secret reports.

Pilot tests taken by 100,000 children in the last 18 months have faced severe problems, giving wildly unpredictable results and exposing children to even more high-pressure testing, the two reports conclude.

The government is piloting the "single level tests" (SLTs) in response to criticisms that the current system of Sats is too stressful for schools and pupils and does not provide high-quality information about their talents.

The scheme was designed to allow pupils to take tests at their own pace between the ages of seven and 14, instead of en masse at the ages of 11 and 14.

The unpublished reports of pilot tests last year, conducted by the National Assessment Agency and five independent academics, and seen by the Guardian, reveal that:

• Results were erratic, with 10-year-olds consistently outperforming 14-year-olds in some tests.

• The agency conducting the pilots urgently appealed for ministers to clarify their plans for the tests. The second report, dated last autumn, says the aims of the test – to assess pupils regardless of their age across a broad curriculum – are "very probably impossible" to achieve.

• By autumn last year ministers had still not addressed concerns raised in an evaluation nearly a year before that warned of "substantial and fundamental" problems.

• The whole programme has been put at risk because the pilots were rushed in too quickly under political pressure.

The schools secretary, Ed Balls, has admitted that the difficulties with the pilots were a factor in his decision last year to abandon national testing of 14-year-olds, but the reports reveal the scale of the problems that the pilots – which cost £8.7m between 2007 and 2009 – have encountered.

Some extraordinary results emerged in the pilots, with secondary pupils consistently scoring significantly worse than primary pupils who were up to five years younger than them when faced with the same maths test. In writing tests, those up to the age of 11 also fared better than older children.

The problem developed from the fact that the tests related to the curriculum learned in primary school, which secondary school pupils had forgotten by the time they were tested. Because the tests are designed to be taken flexibly when children are ready, rather than at a certain age, it raises profound problems about how to match the tests to the curriculum.

The second report also reveals that ministers overruled official advice not to give pupils their marks because of the concerns. There was a "unanimous" opinion among officials that pupils should not be given marks based on the tests in June 2008, but the government insisted on awarding marks. That decision should be understood as a "political/policy level decision", the report says.

The reports blame the rushed introduction of the pilots, announced in January 2007 with the first tests sat in December of the same year. "SLTs should not have been piloted until they had been developed to a point at which they were fit for piloting," the second report, dated last autumn, says. "The timescale for the development of SLTs has been, at best, challenging and, at worst, a risk to the development of valid and reliable assessment instruments."

The first report warns that the tests could add to the burden on pupils instead of reducing it. The authors of the second report also question the "ethics" of the decision to make thousands of pupils sit "high stakes" tests, despite the fact that they had not been properly developed, and raise concerns about the "very substantial" costs of the pilots.

Mary Bousted, general secretary of the Association of Teachers and Lecturers, who has been urging the release of the report for months, said: "It is astonishing that the government has developed SLTs with such inadequate preparation and trialling. All the issues which it was clear were going to be problems from the start have not been addressed properly."

The Department for Children, Schools and Families said another report on assessment for the government, published last month, had stated it was too early to pass judgment on the SLTs but the problems were with the key stage three tests, which have now been scrapped.

The department said: "The Qualifications and Curriculum Authority is currently producing an overarching technical report, covering the first three rounds of SLTs, which will be published later this year. Most importantly, the feedback we have received from teachers and pupils shows a great deal of support for this method of testing. We have always said that the assessment system is not set in stone and we are absolutely committed to continuing – and learning from – these trials."